Help choosing video card for new build

Currently putting together a complete media room. One component will be a PC. My primary rig (at a desk for KB/M) is currently running a 1080ti on a Gsync 1440p 144hz monitor. Zero complaints, I love it.

In the media room will be a Samsung TV most likely which has multiple options for resolutions and refresh rates. It also supports freesync.

1080P @ 120hz
1080P @ 60hz
1080P @ VRR
4k @60hz
4k @ VRR

The VRR options produce the best input lag performance so that is what I am targeting. My issue is choosing the right video card for my needs since using freesync will require AMD (I know that NVidia has started supporting it but haven't read good results outside of the "certified" monitors).

A few games for reference:

Final Fantasy XV
Grand Theft Auto V
Ace Combat 7

I have three choices that fit the budget for the video card in the entire project.

Geforce 2080 @ ~$700 - Best card in my price range but the issue becomes freesync support
Radeon VII @ ~$700 - Just released, driver problems, loud, and buying something that isn't best performance at price just to get true freesync support
Radeon Vega 64 @ $400 - This is my running favorite. Seems to perform well at 4k, may have to back the settings down to med-high on some games. Support for freesync. I also get $300 back into the budget to spend else were.

One note, when I talk about "can a card do 4k" I need to say that 4k /= 4k and super high max settings. Even if you run a game at 4k and medium it generally becomes a better experience on PC than console.

Since it is a new build, aimed at 4k gaming, my order of alternatives:

-Radeon 7. The higher the resolution and settings, the closer radeon 7 comes to 2080, surpassing it on a few more demanding titles. 16GB will make it last longer. I would wait for non-reference coolers. And video prosumers will gladly buy one from you when you upgrade.
-2080.
-2060. It is cheaper, but runs cooler and quieter than Vegas.
-Vega 56 with non reference cooler
-Vega 64 with non reference cooler
-If you can find one, 1080Ti ranks pretty high gaming wise.

You really don't have much choice in the matter. If you want 4K@60 max settings there is only one video card option right now: 2080Ti. They even come with Space Invaders. I'm running a 2080Ti Black edition that set me back about 999 before tax.

Now, I have had a shitload of issues with the 2080Ti series... FYI... However, nothing else comes close to it's performance.

Radeon 7 can do max settings at 4K/60 but will probably have to reduce the settings to maintain FPS
2080 can do max settings at 4K/60 but will probably have to reduce the settings to maintain FPS

If you already have a 1080Ti, there is NO point in either of the above cards (since both the Radeon 7 and the 2080 are essentially as fast as a 1080Ti). The 2080Ti is your only upgrade path.

Given your budget for the new build, try to source a 1080Ti for around 500 bucks from Ebay. At least it will be stable and will not have Space Invaders.